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Noah Smith … on the role of math in economics … suggests that it’s mainly about doing hard stuff to prove that you’re smart. I share much of his cynicism about the profession, but I think he’s missing the main way (in my experience) that mathematical models are useful in economics: used properly, they help you think clearly, in a way that unaided words can’t. Take the centerpiece of my early career, the work on increasing returns and trade. The models … involved a fair bit of work to arrive at what sounds in retrospect like a fairly obvious point. … But this point was only obvious in retrospect. … I … went through a number of seminar experiences in which I had to bring an uncomprehending audience through until they saw the light.

I am convinced that most economath badly fails the cost-benefit test. … Out of the people interested in economics, 95% clearly have a comparative advantage in economic intuition, because they can’t understand mathematical economics at all. …. Even the 5% gain most of their economic understanding via intuition. .. Show a typical economist a theory article, and watch how he “reads” it: … If math is so enlightening, why do even the mathematically able routinely skip the math? .. When mathematical economics contradicts common sense, there’s almost always mathematical sleight of hand at work – a sneaky assumption, a stilted formalization, or bad back-translation from economath to English. … Paul[‘s] … seminar audiences needed the economath because their economic intuition was atrophied from disuse. I can explain Paul’s models to intelligent laymen in a matter of minutes.

Krugman replies:

Yes, there’s a lot of excessive and/or misused math in economics; plus the habit of thinking only in terms of what you can model creates blind spots. … So yes, let’s critique the excessive math, and fight the tendency to equate hard math with quality. But in the course of various projects, I’ve seen quite a lot of what economics without math and models looks like — and it’s not good.

For most questions, the right answer has a simple intuitive explanation. The problem is: so do many wrong answers. Yes we also have intuitions for resolving conflicting intuitions, but we find it relatively easy to self-deceive about such things. Intuitions help people who do not think or argue in good faith to hold to conclusions that fit their ideology, and to not admit they were wrong.

People who instead argue using math are more often forced to admit when they were wrong, or that the best arguments they can muster only support weaker claims than those they made. Similarly, students who enter a field with mistaken intuitions often just do not learn better intuitions unless they are forced to learn to express related views in math. Yes, this typically comes at a huge cost, but it does often work.

We wouldn’t need as much to pay this cost if we were part of communities who argued in good faith. And students (like maybe Bryan) who enter a field with good intuitions may not need as much math to learn more good intuitions from teachers who have them. So for the purpose of drawing accurate and useful conclusions on economics, we could use less math if academics had better incentives for accuracy, such as via prediction markets. Similarly, we could use less math in teaching economics if we better selected students and teachers for good intuitions.

But in fact academia research and teaching put a low priority on accurate useful conclusions, relative to showing off, and math is very helpful for that purpose. So the math stays. In fact, I find it plausible, though hardly obvious, that moving to less math would increase useful accuracy even without better academic incentives or student selection. But groups who do this are likely to lose out in the contest to seem impressive.

A corollary is that if you personally just want to better understand some particular area of economics where you think your intuitions are roughly trustworthy, you are probably better off mostly skipping the math and instead reasoning intuitively. And that is exactly what I’ve found myself doing in my latest project to foresee the rough outlines of the social implications of brain emulations. But once you find your conclusions, then if you want to seem impressive, or to convince those with poor intuitions to accept your conclusions, you may need to put in more math.

## Math: Useful & Over-Used

The article says "But in fact academia research and teaching put a low priority on accurate useful conclusions, relative to showing off, and math is very helpful for that purpose." - exactly correct.

Both real numbers and money are false, because both are not objects of nature. Therefore, whatever you create using math or money, must also be false. Note that money is also a real number, and therefore must be false, since real numbers are false. Falsity of economics is obvious everywhere we look - we see wars, poverty, unemployment, pollution, migration etc. These are all happening because of money. Remove money, and create money-less economy (MLE) all these problems will vanish.

Invalidity of math is very subtle. If you know engineering, it will be obvious for you. For example 3+4=5, is the common case in engineering. This is so because all variables in engineering, and even in economics, are bounded by lower and upper values. In this example 5 is the upper bound. No matter what the result of addition is, the output must be clipped to the upper bound 5. This makes all applications non-linear, but math requires linearity, a very false assumption for nature. The issue is more complex with infinity, another false object of math. Take a look at https://theoryofsouls.wordp... for more details. Under MLE even math will change and become more meaningful.

Mathematical logic is a subject that happens to be useful. It tells you whether certain things are true and others are false. Logic doesn't need any numbers.

Statistics is a subject on it's own and a lot of mathematicians want to have nothing to do with it.

I do care that the garbage collector of my android phone runs well. That has something to do with math, but it's not about numbers.